The muon flux density and the absorbed dose rate that is produced when a high energy electron beam is completely attenuated in matter is calculated by integrating the muon pair production cross section over the photon distribution in the electromagnetic shower.Several cross section and photon track length formulae are examined.The Fermi-Eyges theory of multiple scattering is applied to the case of 1 to 20 GeV muons penetrating thick shields, and the results are folded into the production theory. An 18 GeV electron beam was used to produce muons in order to verify the theory. The results indicate that the theory, even with multiple scattering included, does not correctly predict the shape of the angular dose rate distribution, although integration over the theoretical and experimental curves gives agreement within experimental error.